Graded polynomial identities and Specht property of the Lie algebra sl(2)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Let G be a group. The Lie algebra sl(2) of 2 x 2 traceless matrices over a field K can be endowed up to isomorphism, with three distinct non-trivial G-gradings induced by the groups Z(2), Z(2) x Z(2) and Z. It has been recently shown (Koshlukov, 2008 [8]) that for each grading the ideal of G-graded identities has a finite basis. In this paper we prove that when char(K) = 0, the algebra sl(2) endowed with each of the above three gradings has an ideal of graded identities Id(G)(sl(2)) satisfying the Specht property, i.e., every ideal of graded identities containing Id(G)(sl(2)) is finitely based. (c) 2013 Elsevier Inc. All rights reserved.389622Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)CAPES [BEX 8874/11-5